Results 181 to 190 of about 527,157 (233)

Algebraic Number Theory

1991
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as ...
Martin J. Taylor, A. Fröhlich
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On a problem in algebraic number theory

Mathematical Proceedings of the Cambridge Philosophical Society, 1996
Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq
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Foundations of the Theory of Algebraic Numbers

Nature, 1932
THIS is the first volume of Prof. Hancock's work and is intended as an introduction to the second volume. Its size shows that he is engaged in no light task. His object is to help in making the theory of algebraic numbers more accessible, more attractive, and less difficult.
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Computational Algebra and Number Theory

1995
Preface. 1: Calculating Growth Functions for Groups Using Automata M. Brazil. 2: The Minimal Faithful Degree of a Finite Commutative Inverse Semigroup S. Byleveld, D. Easdown. 3: Generalizations of the Todd-Coxeter Algorithm S. A. Linton. 4: Computing Left Kan Extensions Using the Todd-Coxeter Procedure M. Leeming, R. F. C. Walters. 5: Computing Finite
A. J. Van Der Poorten, Wieb Bosma
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Algebraic Aspects of Number Theory

2014
Chapter 10 discusses some more interesting properties of integers, in particular, properties of prime numbers and primality testing by using the tools of modern algebra, which are not studied in Chap. 1. In addition, the applications of number theory, particularly those directed towards theoretical computer science, are presented.
Mahima Ranjan Adhikari, Avishek Adhikari
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Algebraic Theory of Complex Numbers

1962
Before defining complex numbers let us briefly review the more familiar types of numbers and let us examine why there are different kinds of numbers.
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The Roots of Commutative Algebra in Algebraic Number Theory

Mathematics Magazine, 1995
To put the issues in a broader context, these three number-theoretic problems were instrumental in the emergence of algebraic number theory-one of the two main sources of the modern discipline of commutative algebra.' The other source was algebraic geometry.
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Algebraic Number Theory: Cyclotomy

2018
In this chapter, we return to one of Gauss’s favourite themes, cyclotomic integers, and look at how they were used by Kummer, one of the leaders of the next generation of German number theorists. French and German mathematicians did not keep up-to-date with each other’s work, and for a brief, exciting moment in Paris in 1847 it looked as if the ...
Jeremy Gray, Jeremy Gray
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A Review of Number Theory and Algebra

2015
Elementary number theory may be regarded as a prerequisite for this book, but since we, the authors, want to be nice to you, the readers, we provide a brief review of this theory for those who already have some background on number theory and a crash course on elementary number theory for those who have not.
Harald Niederreiter, Arne Winterhof
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Algebraic Identities in the Theory of Numbers

The American Mathematical Monthly, 1943
(1943). Algebraic Identities in the Theory of Numbers. The American Mathematical Monthly: Vol. 50, No. 9, pp. 535-541.
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